Vol. 50
Latest Volume
All Volumes
PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2016-10-13
Uncertainty Quantification of Radio Propagation Using Polynomial Chaos
By
Progress In Electromagnetics Research M, Vol. 50, 205-213, 2016
Abstract
In this paper we demonstrate how so-called polynomial chaos expansions can be used to create efficient algorithms for uncertainty quantification in some classes of problems related to wave propagation in stochastic environment. We provide an example from telecommunication.
Citation
Mattias Enstedt Niklas Wellander , "Uncertainty Quantification of Radio Propagation Using Polynomial Chaos," Progress In Electromagnetics Research M, Vol. 50, 205-213, 2016.
doi:10.2528/PIERM16062101
http://www.jpier.org/PIERM/pier.php?paper=16062101
References

1. Austin, A. C. M. and C. D. Sarris, "Efficient analysis of geometrical uncertainty in the fdtd method using polynomial chaos with application to microwave circuits," IEEE Transactions on Microwave Theory and Techniques, Vol. 61, No. 12, 4293-4301, Dec. 2013.
doi:10.1109/TMTT.2013.2281777

2. Cameron, R. H. and W. T. Martin, "The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals," Annals of Mathematics, Vol. 48, No. 2, 385-392, 1947.
doi:10.2307/1969178

3. Chauvire, C., J. S. Hesthaven, and L. Lurati, "Computational modeling of uncertainty in time-domain electromagnetics," SIAM Journal on Scientific Computing, Vol. 28, No. 2, 751-775, 2006.
doi:10.1137/040621673

4. Chen, M.-H., Q.-M. Shao, and J. G. Ibrahim, Monte Carlo Methods in Bayesian Computation, Springer, New York, 2000.
doi:10.1007/978-1-4612-1276-8

5. Claerbout, J. F., Imagining the Earth’s Interior, Blackwell Scientific Pub., Palo Alto, CA, 1985.

6. Crank, J. and P. Nicolson, "A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type," Proc. Camb. Phil. Soc., Vol. 43, 50-67, 1947.
doi:10.1017/S0305004100023197

7. Fock, V. A., Electromagnetic Diffraction and Propagation Problems, Pergamon Press, 1965.

8. Holm, P., "Wide-angle shift-map PE for a piecewise linear terrain finite-difference approach," IEEE Transactions on Antennas and Propagation, Vol. 55, 2773-2789, 2007.
doi:10.1109/TAP.2007.905865

9. Jin, J. M., Theory and Computation of Electromagnetic Fields, Wiley, 2011.

10. Leontovich, M. A. and V. A. Fock, "Solution of propagation of electromagnetic waves along earth’s surface by the method of parabolic equations," J. Physics, USSR, Vol. 10, 13-23, 1946.

11. Levy, M., "Parabolic equation methods for electromagnetic wave propagation," IET, 2000.

12. Norton, K. A., "The propagation of radio waves over the surface of the earth and in the upper atmosphere," Proceedings of the Institute of Radio Engineers, Vol. 25, 1203-1236, 1937.

13. Robert, C. P. and G. Casella, Monte Carlo Statistical Methods (Springer Texts in Statistics), Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2005.

14. Smith, R. C., "Uncertainty quantification: Theory, implementation, and applications," Computational Science and Engineering, 2013.

15. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech House, Jun. 2005.

16. Tapper, F. D., "The parabolic approximation method," Wave Propagation and Underwater Acoustics, Vol. 70, 224-287, 1977.
doi:10.1007/3-540-08527-0_5

17. Wan, X. and G. E. Karniadakis, "An adaptive multi-element generalized polynomial chaos method for stochastic differential equations," Journal of Computational Physics, Vol. 209, No. 2, 617-642, 2005.
doi:10.1016/j.jcp.2005.03.023

18. Wiener, N., "The homogeneous chaos," American Journal of Mathematics, Vol. 60, No. 4, 897-936, 1938.
doi:10.2307/2371268